Mourinho's men arrived at Sixfields looking to avoid the ignominy of a fourth straight loss and managed just that, running out 3-1 victors as their quality eventually saw off the spirited League One hosts.
Northampton had looked to be facing a long night when Michael Carrick capped his first appearance since the Community Shield with a sumptuous strike, but the hosts upped the ante as half-time approached and drew a penalty out of Daley Blind.
Alex Revell converted to send a record Sixfields crowd wild, but United regained their advantage through Ander Herrera's thumping effort after 68 minutes.
Substitute Marcus Rashford - brought on early in the second half with Zlatan Ibrahimovic - wrapped up the victory after Adam Smith, much to the goalkeeper's embarrassment, failed to deal with a simple long ball.
It was a comfortable end to what had been at times a nervy night in Northampton, where Wayne Rooney and Chris Smalling were the only survivors in the United line-up from the weekend defeat to Watford.
The visitors started with an intensity lacking in recent matches as Rooney snatched at an early effort, before the captain wasted a glorious chance by directing the ball across the face of goal.
Comfortable in possession and enjoying freedom down the flanks, it was little surprise to see United take a 17th-minute lead, although the way it came about was unusual.
Referee Stuart Attwell awarded an indirect free-kick after goalkeeper Smith inexplicably picked up a back-pass. Rooney's attempt from the set-piece was blocked, but Carrick was on hand to turn home superbly.
The midfielder's first goal since March 2015 seemed to relax the visitors but perhaps too much.
While the offside flag prevented Rooney extending United's lead after a Timothy Fosu-Mensah header hit the crossbar, Northampton were becoming an increasing threat.
United academy graduate Kenji Gorre was the first to really threaten for the hosts, making the most of a fine Northampton move and lax United defending to hit an effort that was tipped onto the bar.
Zander Diamond headed over from the resulting corner as Rob Page's side pushed for a leveller that would arrive after Blind brought down Sam Hoskins in the box.
Experienced striker Revell capitalised, sending Sergio Romero the wrong way and the home fans delirious.
The Sixfields crowd claimed another penalty against the back-up United goalkeeper soon afterwards, but it came to nothing as the half-time whistle brought welcome respite for the visitors.
United emerged from the break strongly but were struggling to threaten Smith, leading Mourinho to bring on Rashford and Ibrahimovic within 10 minutes of the restart.
Herrera hit the post from distance soon after and found the net the next time he tried his luck from long range, meeting a Rashford pass with a low strike that flew past Smith in front of the 944 visiting fans.
There was little the Northampton goalkeeper could do about that, but his embarrassment was clear as United racked up a third.
Rashford chased Herrera's hacked clearance - a lost cause that became a gift as Smith hesitated and missed the ball, allowing the substitute to smash into an empty net.
Smith denied Marouane Fellaini as United chased a fourth but it was Northampton that ended the match on the attack, albeit unable to reduce the deficit.
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